> James wrote: Given that equal temperament divides up the Wolf into a
wolf-pup at every half-step, equal temperament IS equally-beating. It's also
the only temperament I'm aware of that's BOTH meantone (albeit with a comma
at every half-step) AND cyclic.
You are absolutely correct James!! ...
... unless, of course, you re-define (as some scholars do) terms as follows:
"Meantone temperament": a temperament with 11 fifths narrowed by the same
amount, and the remaining fifth wide to close the circle.
[As we all know, if the remaining fifth is identical to the others, you are
not having meantone but Equal Temperament instead. If the fifths are pure
and the remaining fifth is narrow, you get Pythagorean intonation...]
"Circular temperament": a UNEQUAL temperament where all the fifths and all
the major thirds are playable (although a few barely so) without ever
running into anything like the classical meantone temperament wolves, or
without ever tempering all the fifths identically.
Finally, let me observe something also noted by some scholars: if you tune
11th fifths reduced by 1/11th of the Syntonic comma (instead of the very
similar but not identical 1/12th of the Pytagorean comma), and also a few
other similar comma fractions, you get a temperament that is indeed BOTH
meantone AND circular, yet is not Equal Temperament. However, since hardly
anybody today or in antiquity put something like this in to practice, your
assertion is valid to all practical effects.
Kind regards,
CDV
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